Solve the problem using a system of equations: Donnette found a widescreen TV at a garage sale, but she isn't sure if it will fit in her entertainment center. The TV is 50". The size of a TV is measured on the diagonal of the screen, and a widescreen has a length that is larger than the width. The screen also has an area of 1,200 square inches. What are the length and width of the TV screen?
length=___inches, width=___ inches
Answers
Check the picture below.
[tex]\begin{cases} L^2+w^2=50^2\\ Lw = 1200\\[-0.5em] \hrulefill\\ L^2+w^2=2500\\ L=\sqrt{2500-w^2} \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{\sqrt{2500-w^2}~w=1200} \\\\\\ \stackrel{\textit{squaring both sides}}{w^2(2500-w^2) = 1200^2}\implies 2500w^2-w^4=1440000 \\\\\\ 0=w^4-2500w^2+1440000\implies 0=\stackrel{\textit{tis a quadratic}}{(w^2)^2-2500w^2+1440000}[/tex]
[tex]0=(w^2-900)(w^2-1600)\implies \begin{cases} 0=w^2-900\\ 900=w^2\\ \sqrt{900}=w\\ \boxed{30=w}\\[-0.5em] \hrulefill\\ 0=w^2-1600\\ 1600=w^2\\ \sqrt{1600}=w\\ \boxed{40=w} \end{cases} \\\\\\ \stackrel{\textit{we know that}}{L = \sqrt{2500 - w^2}}\implies \begin{cases} L=\sqrt{2500-30^2}\\ \boxed{L=40}\\[-0.5em] \hrulefill\\ L=\sqrt{2500-40^2}\\ \boxed{L = 30} \end{cases}[/tex]
The length of the given TV is 40 inches and width of the given TV is 30 inches.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
The area of rectangular shape TV is 1,200 square inches.
The TV is 50".
Now, L²+W²=50² ----------(I)
L×W=1200 ----------(II)
L²+W²=2500
⇒ L²=2500-W²
⇒ L=√(2500-W²)
Substitute L=1200/W in L=√(2500-W²), we get
1200/W=√(2500-W²)
Squaring on both the sides we get
1440000/W² =2500-W²
⇒ 1440000=2500W²-[tex]W^4[/tex]
⇒ [tex]W^4[/tex]-2500W²+1440000=0
⇒ (W²)²-2500W²+1440000=0
⇒ (W²)²-900W²-1600W²+1440000=0
⇒ W²(W²-900)-1600(W²-1600)=0
⇒ (W²-1600)(W²-900)=0
⇒ W²-1600=0 and W²-900=0
⇒ W²=1600 and W²=900
⇒ W=±40 and W=±30
So, W=40, -40, 30, -30
Length =1200/W =40 or 30
Therefore, the length of the TV is 40 inches and width is 30 inches.
To learn more about the area of a rectangle visit:
https://brainly.com/question/20693059.
#SPJ2
Related Questions
Please any math experts help thanks you
Answers
Answer:
[tex]\frac{p^2-25}{p^2-10p+25}[/tex]
We can factorise the numerator with the difference of squares formula:[tex]x^2-y^2=(x+y)(x-y)[/tex]
-----------------------------
[tex]\frac{p^2-5^2}{p^2-10p+25} =\frac{(p+5)(p-5)}{p^2-10p+25}[/tex]
Now we can factorise the denominator:
[tex]\frac{(p+5)(p-5)}{p^2-10p+25} =\frac{(p+5)(p-5)}{(p-5)^2}[/tex]
[tex]\frac{(p+5)(p-5)}{(p-5)^2} =\frac{(p+5)(p-5)}{(p-5)(p-5)}[/tex]
Cancel out the common factor of (p-5):
[tex]\frac{(p+5)(p-5)}{(p-5)(p-5)} =\frac{(p+5)}{(p-5)}[/tex]
100 POINT QUESTION!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve 2x2 – 6x + 10 = 0 by completing the square.
Question 10 options:
A)
x = 3∕2 + 1∕2 i, x = 3∕2 – 1∕2i
B)
x = 3 + i, x = 3 – i
C)
x = 3∕2 + i , x = 3∕2 – i
D)
x = 3 + i, x = 3 – i
Answers
Answer:
Ok I don't know waht you mean but the answer is
Step-by-step explanation:
Answer:
x=3/2±(√11)2
x=1.5+1.65831i
x=1.5−1.65831i
Find the Solution for
2x^22−6x+10=0
using the Quadratic Formula where
a = 2, b = -6, and c = 10
x=(−b±√(b^2−4ac))/2a
x=(−(−6)±√((−6)2−4(2)(10)))2(2)
x=(6±√(36−80))/4
x=(6±√−44)/4
The discriminant b^2−4ac<0
so, there are two complex roots.
Simplify the Radical:
x=(6±2√11 i)/4
x=6/4±(2√11 i)4
Simplify fractions and/or signs:
x=3/2±(√11)2
which becomes
x=1.5+1.65831i
x=1.5−1.65831i
use the given circle. Find the length s to the nearest tenth A. 33.5 cm B. 8.4 cm C. 16.8 cm D. 5.3 cm
Answers
Answer:
16.8
Step-by-step explanation:
s = ∅ × r
= 2π/3 × 8
= 16/3 * π
= 16.75516
= 16.8
Answer:
C.) 16.8 is your answer
Step-by-step explanation:
4. If the paint costs $30 per gallon and you need to spend $60 on supplies, and you can
save $45 per month, in how many months will you have enough money for the project?
Answers
Step-by-step explanation:
if I understand this right, then you need paint and additional supplies.
but I don't see any information indicating how many gallons of paint I will need.
so, I can go only with the 1 gallon specified.
so,
1×30 + 60 = $90
we can save $45 per month.
then we need
90 / 45 = 2
months to have enough money.
please update the numbers to how many gallons you really need, and then take that result and divide it by the 45 savings per month.
C is wrong help me please
Answers
Answer:
A
Step-by-step explanation:
x from 0 < x < 2 is wrong because < means goes to but does not equal that value, and [tex]\leq[/tex] means it INCLUDES that value. Because the function includes it (not an open hole), you should choose A.
Jorge bikes to school each day. If he can travel 33 miles in 11 hours, how fast does he travel in one
hour?
Write a symbolic expression using division that represents this problem.
Calculated Answer:
miles per hour
Answers
33 miles divided by 11 hours will give you the mile per hour traveled.
Answer: 3 miles per hr
The high temperatures for the first five days in December were as follows 28, 3, -2, -4 and 12. What is the average temperature.
Answers
Answer:
28 +3 +2+4+12=49
49÷5=9.8
At a concert the ratio of adults to children is 4:5. There are 720 children in a concert how many adults are there?
BRAINLIEST QUEATION !!
Answers
Answer:
576 adults
Step-by-step explanation:
The 5 part of the ratio relates to 720 children, then
720 ÷ 5 = 144 ← value of 1 part of the ratio , then
4 parts = 4 × 144 = 576 ← number of adults
Answer:
576
Step-by-step explanation:
Adults : Children
4 : 5
x : 720
Let the number of adults be x.
Use cross multiplication.
[tex]4 : 5\\ x : 720\\[/tex]
[tex]4 *720=5*x[/tex]
[tex]\frac{4*720}{5} =\frac{5x}{5}[/tex]
4 × 144 = x
576 = x
Hope this helps you.
Let me know if you have any other questions :-)
solve for x someone pls help
Answers
Answer:
50+90+3x+1=180.....................
helpp pls
4 pairs of shoes cost $80. What is the cost of 7 pairs of shoes ?
A
$130
B
$150
C
$145
D
$140
Answers
Answer:
D. 140
Step-by-step explanation:
4 / 80 = 20
20 * 7 = 140
therefore, 140 is the answer
Answer:
140
Step-by-step explanation:
Please help answer this! I will give you 10 pts! :DD ( please don't say non-sense I really need the answer! )
Answers
Answer:
angle a = angle bac = 90 degrees
angle b = angle abc
angle c = angle acb
Solve please
May God bless you
Answers
Answer:
We will use a Pythagorean identity and alegbra to prove this.
sin^2 + cos^2 = 1, dividing by cos^2 gives
tan^2 + 1 = sec^2.
Now, breaking down the fraction into parts and simplifying gives:
(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4
Now use difference of squares factoring from alegbra.
= (sec^2 + tan^2)*(sec^2 - tan^2)
By rewriting our Pythagorean identity to
sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,
we can finish the problem.
= (sec^2 + tan^2) * 1 = sec^2 + tan^2
= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.
What is the solution to -4(8- 3x) >6x - 8?
A)x>-4/3
B)x<-4/3
C)x>4
D)x<4
Answers
I think you got your answer
increase R700 in the ratio 3:2
Answers
Answer:
3 over5 multiplied by 320 equals 192
PLEASR HELP REWARDING A LOT
Answers
Answer:
(6, 10)
Step-by-step explanation:
You found (6, 4)
The second would be
(6, 10) making BD || to CA
whats the answer can someone answer please
Answers
Answer:
21. 2x + 28
22. 18a - 17b
23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.
24. 8.8888888888889 × 10^{0}
Step-by-step explanation:
a Rose Garden is formed by joining a rectangle and a semicircle the rectangle is 33 ft long and 26 ft wide. If the gardener wants to build a fence around the garden how many feet of fence are required?
Answers
We know that the area of a rectangle is the length times width, or
20
⋅
32
in this example:
20
⋅
32
=
640
So the area of the rectangle is
640
f
t
2
.
You may not know the area of a semicircle, but that's fine
−
we know the area of a circle, or
π
r
2
.
Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by
2
:
So the area of a semicircle is
π
r
2
2
.
The question asks for
π
to just be
3.14
, so instead the equation is
A
=
3.14
r
2
2
The picture gives the diameter of the circle.
To find the radius, or
r
, we divide the diameter by
2
:
20
2
=
10
Now we can solve for the area of the semicircle:
3.14
(
10
)
2
2
3.14
(
100
)
2
314
2
157
f
t
2
Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:
640
+
157
=
797
f
t
2
A woman can invest some money at 10% simple interest or at 8% compound interest. If
she invests $8000 for 3 years, find which is the more profitable investment and by how much.
Answers
Answer:
3/12 percent
Step-by-step explanation:
The initial amount of money that is deposited into an account or that is borrowed is called what
Answers
Answer:
Step-by-step explanation:
Answer: In the context of borrowing, principal is the initial size of a loan or a bond (the amount the bond issuer must repay). In the context of investing, principal is the original sum committed to the purchase of assets—independent of any earnings or interest.
Find the volume of this cylinder.
Give your answer to 1 decimal place.
11 cm
io
14 cm
Answers
Answer:
1330.5 cm³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . . for radius r and height h
The radius of the given cylinder is 1/2(11 cm) = 5.5 cm. Filling in the formula values, we have ...
V = π(5.5 cm)²(14 cm) = 423.5π cm³ ≈ 1330.5 cm³
The volume of the cylinder is about 1330.5 cm³.
Answer:
1330.5
Step-by-step explanation:
Radius is half of diameter (11), so 5.5 was the other number I plugged in.
Write the equation of the line that passes through the points (-9,9) and (8, -2).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answers
Answer:
y + 2 = (11/17)(x - 8)
Step-by-step explanation:
Working with the x- and y-components of the given points, we see that the x component increases by 17 and the y-component decreases by 11. Thus, the slope of this line is m = rise / run, or 11/17.
Start with the general point-slope form: y - k = m(x - h) and use the coordinates of the 2nd point for h and k in this equation:
y + 2 = (11/17)(x - 8)
This is based on the point (-2, 8)
and the slope 11/17.
This result is the desired equation in point-slope form. If we wish to reduce this, proceed as follows:
17(y + 2) = 11x - 88, or 17y + 34 = 11x - 88
This last result simplifies to 17y = 11x - 54, or y = (11/17)x -54/17 (which is in slope-intercept form).
toby used 4 inches of tape to wrap a gift how much tape will he need to wrap 5 more of the same gift?
Answers
Answer:
20
Step-by-step explanation:
4*5 = 20%
If AD = 12 and BD = 14, what is CD?
Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
a. 7
b. 10.29
C. 12.54
d. 16.33
Answers
Answer: D. 16.33
Step-by-step explanation:
Heyyyyyyyyyyyyyyyyyyyyyyyyyy!
Answers
8 m good wire how long is the wire in millimeters
Answers
Answer:
Converting m to mm
=> 1 m = 1000 mm
=> 8 m = 8000 mm
Therefore,
The wire will be 8000 mm long.
Hope it helps you...
Please mark as brainlliest!!!
Can anyone help me if you get it right i'll give 30!
Answers
[tex]LHS \\ = 8 + 7 - {2}^{2} \\ = 8 + 7 - 4 \\ = 15 - 4 \\ = 11[/tex]
[tex]RHS \\ = {3}^{2} + 2 \\ = 9 + 2 \\ 11[/tex]
So, LHS = RHS
Answer:=
Hope it helps.
Do comment if you have any query.
Answer:
Below!
Step-by-step explanation:
Let's try the 'equal' sign for this equation.
8 + 7 - 2² = 3² + 2Remember, when it comes to simplifying, exponents come first. This means that we need to simplify the exponents first.
=> 8 + 7 - (2 x 2) = 9 + 2=> 15 - 4 = 9 + 2=> 11 = 11Since the LHS and the RHS are equal, the 'equal' sign will fit into the equation. Hence, this is proven as true. Let's try the 'not equal' sign.
=> 8 + 7 - 2² ≠ 3² + 2=> 15 - 4 ≠ 9 + 2=> 11 ≠ 11Now, this is a definite false. The 'not equal' sign is used when two values are not equal to each other, however, in this situation, 11 does equal 11. In between them is a 'not equal' sign. Hence, this is proven false.
We can conclude that the sign you are looking for is an 'equal' sign.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Please Help, This is Due in 4 Hours.
At the deli counter, Dalton bought 0.38 of a pound of roast beef and 0.7 of a pound of ham. Compare the amounts of roast beef and ham that Dalton bought.
Record the comparison using the <, >, or = symbol and explain how you know.
Answers
Answer:
0.38 < 0.70
Step-by-step explanation:
Matthew poured 28 quart of lemonade from a pitcher into a smaller container. There was 58 quart left in the pitcher. What amount of lemonade did Matthew originally have in the pitcher?
Answers
Answer:
86 quarts
Step-by-step explanation:
If you took away 28 quarts and were left with 58 quarts then you add the two numbers to get 86 quarts which is what you started with.
Evaluate.
(1/5) −1 ⋅ 4^0
0
1
5
20
Answers
Answer:
-1519 4/5
-1519.8
-7599/5
Step-by-step explanation:
(1/5) - 1 • 1
(1/5) -1
(1/5) -1/1
(1/5) - (5/5)
(1-5/5)
-4/5
The equation of two functions f(x) And g(x) are typed into a graphing calculator to see both graphs on the same coordinate plane. The graphs shown below represents the two functions.
Which are approximate solutions of the equation f(x)=g(x) Select all that apply.
A. 6
B. 0.7
C. 0
D. 4.6
Answers
Answer:
The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g